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Find the volume of the solid formed when the area bound by the curve y=4x^2 and the x axis is rotated one complete revolution about the y axis
 one year ago
 one year ago
Find the volume of the solid formed when the area bound by the curve y=4x^2 and the x axis is rotated one complete revolution about the y axis
 one year ago
 one year ago

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sauravshakyaBest ResponseYou've already chosen the best response.0
first find the critical points and use integration
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
or just consider one side of it
 one year ago

virtusBest ResponseYou've already chosen the best response.0
can you just tell me the answer , because i am getting the wrong answer. I got 16 pi units but the answer is 8 pi units and i don't know where i went wrong.
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
please dont ask for "just an answer"
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1342094312271:dw this can be done by shells or disks; which way are you most comfortable with?
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
i think i know why youre twice as big as the answer; your prolly integrating the whole thing across
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
your in effect sweeping the same volume twice when you do that
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
the answer is 8pi
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1342094460320:dw if we do shells:\[\int_{0}^{2}2pix(4x^2)dx\] \[2pi\int_{0}^{2}x(4x^2)dx\] \[2pi\int_{0}^{2}4xx^3\ dx\] \[2pi\left(\frac{1}{2}4x^2\frac{1}{4}x^4\right)_{0}^{2}\]
 one year ago

virtusBest ResponseYou've already chosen the best response.0
oh i think i understand. I apologise amistre64 if i sounded rude before. I had no intentions whatsoever to offend you.
 one year ago

virtusBest ResponseYou've already chosen the best response.0
@amistre64 i thought it was around y axis, shouldn't be dy not dx ?
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
depends on your method; i used the shell method, which opens up along the x axis the disc method would travel along the y
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
teh disc method we would have to convert y=x into its inverse x=y, which isnt that hard to do, but just takes extra steps :)
 one year ago

virtusBest ResponseYou've already chosen the best response.0
oh i see, so for the shell method where does the x come from in x(4x^2)
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
think of the shell method as finding the area of a sheet of paper, or a flattened out tin can. the width of the paper is the circumference of the base circledw:1342095061762:dw the height of the paper is the function that it hits along the way. Area = base (2pi x) * height (f(x))
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
dw:1342095194082:dw
 one year ago

virtusBest ResponseYou've already chosen the best response.0
OH I GET IT NOW ! thanks @amistre64
 one year ago
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